A method and system for electrochemically machining a hollow body of a metal or a metal alloy. An electrode is positioned within a hollow body including a metal or metal alloy, where the hollow body has a variable internal diameter. The hollow body is oriented vertically, with the electrode oriented vertically therein. The hollow body is at least partially filled with an aqueous, acidic electrolyte solution, the electrolyte solution being devoid of hydrofluoric acid and having a viscosity less than 15 cP. An electric current is passed between the hollow body and the electrode, where the electric current includes a plurality of anodic pulses and a plurality of cathodic pulses, and where the cathodic pulses are interposed between at least some of the anodic pulses.